The economics of interstellar travel

Dec 19 JDN 2459568

Since these are rather dark times—the Omicron strain means that COVID is still very much with us, after nearly two years—I thought we could all use something a bit more light-hearted and optimistic.

In 1978 Paul Krugman wrote a paper entitled “The Theory of Interstellar Trade”, which has what is surely one of the greatest abstracts of all time:

This paper extends interplanetary trade theory to an interstellar setting. It is chiefly concerned with the following question: how should interest charges on goods in transit be computed when the goods travel at close to the speed of light? This is a problem because the time taken in transit will appear less to an observer travelling with the goods than to a stationary observer. A solution is derived from economic theory, and two useless but true theorems are proved.

The rest of the paper is equally delightful, and well worth a read. Of particular note are these two sentences, which should give you a feel: “The rest of the paper is, will be, or has been, depending on the reader’s inertial frame, divided into three sections.” and “This extension is left as an exercise for interested readers because the author does not understand general relativity, and therefore cannot do it himself.”

As someone with training in both economics and relativistic physics, I can tell you that Krugman’s analysis is entirely valid, given its assumptions. (Really, this is unsurprising: He’s a Nobel Laureate. One could imagine he got his physics wrong, but he didn’t—and of course he didn’t get his economics wrong.) But, like much high-falutin economic theory, it relies upon assumptions that are unlikely to be true.

Set aside the assumptions of perfect competition and unlimited arbitrage that yield Krugman’s key result of equalized interest rates. These are indeed implausible, but they’re also so standard in economics as to be pedestrian.

No, what really concerns me is this: Why bother with interstellar trade at all?

Don’t get me wrong: I’m all in favor of interstellar travel and interstellar colonization. I want humanity to expand and explore the galaxy (or rather, I want that to be done by whatever humanity becomes, likely some kind of cybernetically and biogenetically enhanced transhumans in endless varieties we can scarcely imagine). But once we’ve gone through all the effort to spread ourselves to distant stars, it’s not clear to me that we’d ever have much reason to trade across interstellar distances.

If we ever manage to invent efficient, reliable, affordable faster-than-light (FTL) travel ala Star Trek, sure. In that case, there’s no fundamental difference between interstellar trade and any other kind of trade. But that’s not what Krugman’s paper is about, as its key theorems are actually about interest rates and prices in different inertial reference frames, which is only relevant if you’re limited to relativistic—that is, slower-than-light—velocities.

Moreover, as far as we can tell, that’s impossible. Yes, there are still some vague slivers of hope left with the Alcubierre Drive, wormholes, etc.; but by far the most likely scenario is that FTL travel is simply impossible and always will be.

FTL communication is much more plausible, as it merely requires the exploitation of nonlocal quantum entanglement outside quantum equilibrium; if the Bohm Interpretation is correct (as I strongly believe it is), then this is a technological problem rather than a theoretical one. At best this might one day lead to some form of nonlocal teleportation—but definitely not FTL starships. Since our souls are made of software, sending information can, in principle, send a person; but we almost surely won’t be sending mass faster than light.

So let’s assume, as Krugman did, that we will be limited to travel close to, but less than, the speed of light. (I recently picked up a term for this from Ursula K. Le Guin: “NAFAL”, “nearly-as-fast-as-light”.)

This means that any transfer of material from one star system to another will take, at minimum, years. It could even be decades or centuries, depending on how close to the speed of light we are able to get.

Assuming we have abundant antimatter or some similarly extremely energy-dense propulsion, it would reasonable to expect that we could build interstellar spacecraft that would be capable of accelerating at approximately Earth gravity (i.e. 1 g) for several years at a time. This would be quite comfortable for the crew of the ship—it would just feel like standing on Earth. And it turns out that this is sufficient to attain velocities quite close to the speed of light over the distances to nearby stars.

I will spare you the complicated derivation, but there are well-known equations which allow us to convert from proper acceleration (the acceleration felt on a spacecraft, i.e. 1 g in this case) to maximum velocity and total travel time, and they imply that a vessel which was constantly accelerating at 1 g (speeding up for the first half, then slowing down for the second half) could reach most nearby stars within about 50 to 100 years Earth time, or as little as 10 to 20 years ship time.

With higher levels of acceleration, you can shorten the trip; but that would require designing ships (or engineering crews?) in such a way as to sustain these high levels of acceleration for years at a time. Humans can sustain 3 g’s for hours, but not for years.

Even with only 1-g acceleration, the fuel costs for such a trip are staggering: Even with antimatter fuel you need dozens or hundreds of times as much mass in fuel as you have in payload—and with anything less than antimatter it’s basically just not possible. Yet there is nothing in the laws of physics saying you can’t do it, and I believe that someday we will.

Yet I sincerely doubt we would want to make such trips often. It’s one thing to send occasional waves of colonists, perhaps one each generation. It’s quite another to establish real two-way trade in goods.

Imagine placing an order for something—anything—and not receiving it for another 50 years. Even if, as I hope and believe, our descendants have attained far longer lifespans than we have, asymptotically approaching immortality, it seems unlikely that they’d be willing to wait decades for their shipments to arrive. In the same amount of time you could establish an entire industry in your own star system, built from the ground up, fully scaled to service entire planets.

In order to justify such a transit, you need to be carrying something truly impossible to produce locally. And there just won’t be very many such things.

People, yes. Definitely in the first wave of colonization, but likely in later waves as well, people will want to move themselves and their families across star systems, and will be willing to wait (especially since the time they experience on the ship won’t be nearly as daunting).

And there will be knowledge and experiences that are unique to particular star systems—but we’ll be sending that by radio signal and it will only take as many years as there are light-years between us; or we may even manage to figure out FTL ansibles and send it even faster than that.

It’s difficult for me to imagine what sort of goods could ever be so precious, so irreplaceable, that it would actually make sense to trade them across an interstellar distance. All habitable planets are likely to be made of essentially the same elements, in approximately the same proportions; whatever you may want, it’s almost certainly going to be easier to get it locally than it would be to buy it from another star system.

This is also why I think alien invasion is unlikely: There’s nothing they would particularly want from us that they couldn’t get more easily. Their most likely reason for invading would be specifically to conquer and rule us.

Certainly if you want gold or neodymium or deuterium, it’ll be thousands of times easier to get it at home. But even if you want something hard to make, like antimatter, or something organic and unique, like oregano, building up the industry to manufacture a product or the agriculture to grow a living organism is almost certainly going to be faster and easier than buying it from another solar system.

This is why I believe that for the first generation of interstellar colonists, imports will be textbooks, blueprints, and schematics to help build, and films, games, and songs to stay entertained and tied to home; exports will consist of of scientific data about the new planet as well as artistic depictions of life on an alien world. For later generations, it won’t be so lopsided: The colonies will have new ideas in science and engineering as well as new art forms to share. Billions of people on Earth and thousands or millions on each colony world will await each new transmission of knowledge and art with bated breath.

Long-distance trade historically was mainly conducted via precious metals such as gold; but if interstellar travel is feasible, gold is going to be dirt cheap. Any civilization capable of even sending a small intrepid crew of colonists to Epsilon Eridani is going to consider mining asteroids an utterly trivial task.

Will such transactions involve money? Will we sell these ideas, or simply give them away? Unlike my previous post where I focused on the local economy, here I find myself agreeing with Star Trek: Money isn’t going to make sense for interstellar travel. Unless we have very fast communication, the time lag between paying money out and then seeing it circulate back will be so long that the money returned to you will be basically worthless. And that’s assuming you figure out a way to make transactions clear that doesn’t require real-time authentication—because you won’t have it.

Consider Epsilon Eridani, a plausible choice for one of the first star systems we will colonize. That’s 10.5 light-years away, so a round-trip signal will take 21 years. If inflation is a steady 2%, that means that $100 today will need to come back as $151 to have the same value by the time you hear back from your transaction. If you had the option to invest in a 5% bond instead, you’d have $279 by then. And this is a nearby star.

It would be much easier to simply trade data for data, maybe just gigabyte for gigabyte or maybe by some more sophisticated notion of relative prices. You don’t need to worry about what your dollar will be worth 20 years from now; you know how much effort went into designing that blueprint for an antimatter processor and you know how much you’ll appreciate seeing that VR documentary on the rings of Aegir. You may even have in mind how much it cost you to pay people to design prototypes and how much you can sell the documentary for; but those monetary transactions will be conducted within your own star system, independently of whatever monetary system prevails on other stars.

Indeed, it’s likely that we wouldn’t even bother trying to negotiate how much to send—because that itself would have such overhead and face the same time-lags—and would instead simply make a habit of sending everything we possibly can. Such interchanges could be managed by governments at each end, supported by public endowments. “This year’s content from Epsilon Eridani, brought to you by the Smithsonian Institution.”

We probably won’t ever have—or need, or want—huge freighter ships carrying containers of goods from star to star. But with any luck, we will one day have art and ideas from across the galaxy shared by all of the endless variety of beings humanity has become.

What good are macroeconomic models? How could they be better?

Dec 11, JDN 2457734

One thing that I don’t think most people know, but which immediately obvious to any student of economics at the college level or above, is that there is a veritable cornucopia of different macroeconomic models. There are growth models (the Solow model, the Harrod-Domar model, the Ramsey model), monetary policy models (IS-LM, aggregate demand-aggregate supply), trade models (the Mundell-Fleming model, the Heckscher-Ohlin model), large-scale computational models (dynamic stochastic general equilibrium, agent-based computational economics), and I could go on.

This immediately raises the question: What are all these models for? What good are they?

A cynical view might be that they aren’t useful at all, that this is all false mathematical precision which makes economics persuasive without making it accurate or useful. And with such a proliferation of models and contradictory conclusions, I can see why such a view would be tempting.

But many of these models are useful, at least in certain circumstances. They aren’t completely arbitrary. Indeed, one of the litmus tests of the last decade has been how well the models held up against the events of the Great Recession and following Second Depression. The Keynesian and cognitive/behavioral models did rather well, albeit with significant gaps and flaws. The Monetarist, Real Business Cycle, and most other neoclassical models failed miserably, as did Austrian and Marxist notions so fluid and ill-defined that I’m not sure they deserve to even be called “models”. So there is at least some empirical basis for deciding what assumptions we should be willing to use in our models. Yet even if we restrict ourselves to Keynesian and cognitive/behavioral models, there are still a great many to choose from, which often yield inconsistent results.

So let’s compare with a science that is uncontroversially successful: Physics. How do mathematical models in physics compare with mathematical models in economics?

Well, there are still a lot of models, first of all. There’s the Bohr model, the Schrodinger equation, the Dirac equation, Newtonian mechanics, Lagrangian mechanics, Bohmian mechanics, Maxwell’s equations, Faraday’s law, Coulomb’s law, the Einstein field equations, the Minkowsky metric, the Schwarzschild metric, the Rindler metric, Feynman-Wheeler theory, the Navier-Stokes equations, and so on. So a cornucopia of models is not inherently a bad thing.

Yet, there is something about physics models that makes them more reliable than economics models.

Partly it is that the systems physicists study are literally two dozen orders of magnitude or more smaller and simpler than the systems economists study. Their task is inherently easier than ours.

But it’s not just that; their models aren’t just simpler—actually they often aren’t. The Navier-Stokes equations are a lot more complicated than the Solow model. They’re also clearly a lot more accurate.

The feature that models in physics seem to have that models in economics do not is something we might call nesting, or maybe consistency. Models in physics don’t come out of nowhere; you can’t just make up your own new model based on whatever assumptions you like and then start using it—which you very much can do in economics. Models in physics are required to fit consistently with one another, and usually inside one another, in the following sense:

The Dirac equation strictly generalizes the Schrodinger equation, which strictly generalizes the Bohr model. Bohmian mechanics is consistent with quantum mechanics, which strictly generalizes Lagrangian mechanics, which generalizes Newtonian mechanics. The Einstein field equations are consistent with Maxwell’s equations and strictly generalize the Minkowsky, Schwarzschild, and Rindler metrics. Maxwell’s equations strictly generalize Faraday’s law and Coulomb’s law.
In other words, there are a small number of canonical models—the Dirac equation, Maxwell’s equations and the Einstein field equation, essentially—inside which all other models are nested. The simpler models like Coulomb’s law and Newtonian mechanics are not contradictory with these canonical models; they are contained within them, subject to certain constraints (such as macroscopic systems far below the speed of light).

This is something I wish more people understood (I blame Kuhn for confusing everyone about what paradigm shifts really entail); Einstein did not overturn Newton’s laws, he extended them to domains where they previously had failed to apply.

This is why it is sensible to say that certain theories in physics are true; they are the canonical models that underlie all known phenomena. Other models can be useful, but not because we are relativists about truth or anything like that; Newtonian physics is a very good approximation of the Einstein field equations at the scale of many phenomena we care about, and is also much more mathematically tractable. If we ever find ourselves in situations where Newton’s equations no longer apply—near a black hole, traveling near the speed of light—then we know we can fall back on the more complex canonical model; but when the simpler model works, there’s no reason not to use it.

There are still very serious gaps in the knowledge of physics; in particular, there is a fundamental gulf between quantum mechanics and the Einstein field equations that has been unresolved for decades. A solution to this “quantum gravity problem” would be essentially a guaranteed Nobel Prize. So even a canonical model can be flawed, and can be extended or improved upon; the result is then a new canonical model which we now regard as our best approximation to truth.

Yet the contrast with economics is still quite clear. We don’t have one or two or even ten canonical models to refer back to. We can’t say that the Solow model is an approximation of some greater canonical model that works for these purposes—because we don’t have that greater canonical model. We can’t say that agent-based computational economics is approximately right, because we have nothing to approximate it to.

I went into economics thinking that neoclassical economics needed a new paradigm. I have now realized something much more alarming: Neoclassical economics doesn’t really have a paradigm. Or if it does, it’s a very informal paradigm, one that is expressed by the arbitrary judgments of journal editors, not one that can be written down as a series of equations. We assume perfect rationality, except when we don’t. We assume constant returns to scale, except when that doesn’t work. We assume perfect competition, except when that doesn’t get the results we wanted. The agents in our models are infinite identical psychopaths, and they are exactly as rational as needed for the conclusion I want.

This is quite likely why there is so much disagreement within economics. When you can permute the parameters however you like with no regard to a canonical model, you can more or less draw whatever conclusion you want, especially if you aren’t tightly bound to empirical evidence. I know a great many economists who are sure that raising minimum wage results in large disemployment effects, because the models they believe in say that it must, even though the empirical evidence has been quite clear that these effects are small if they are present at all. If we had a canonical model of employment that we could calibrate to the empirical evidence, that couldn’t happen anymore; there would be a coefficient I could point to that would refute their argument. But when every new paper comes with a new model, there’s no way to do that; one set of assumptions is as good as another.

Indeed, as I mentioned in an earlier post, a remarkable number of economists seem to embrace this relativism. “There is no true model.” they say; “We do what is useful.” Recently I encountered a book by the eminent economist Deirdre McCloskey which, though I confess I haven’t read it in its entirety, appears to be trying to argue that economics is just a meaningless language game that doesn’t have or need to have any connection with actual reality. (If any of you have read it and think I’m misunderstanding it, please explain. As it is I haven’t bought it for a reason any economist should respect: I am disinclined to incentivize such writing.)

Creating such a canonical model would no doubt be extremely difficult. Indeed, it is a task that would require the combined efforts of hundreds of researchers and could take generations to achieve. The true equations that underlie the economy could be totally intractable even for our best computers. But quantum mechanics wasn’t built in a day, either. The key challenge here lies in convincing economists that this is something worth doing—that if we really want to be taken seriously as scientists we need to start acting like them. Scientists believe in truth, and they are trying to find it out. While not immune to tribalism or ideology or other human limitations, they resist them as fiercely as possible, always turning back to the evidence above all else. And in their combined strivings, they attempt to build a grand edifice, a universal theory to stand the test of time—a canonical model.

Nuclear power is safe. Why don’t people like it?

Sep 24, JDN 2457656

This post will have two parts, corresponding to each sentence. First, I hope to convince you that nuclear power is safe. Second, I’ll try to analyze some of the reasons why people don’t like it and what we might be able to do about that.

Depending on how familiar you are with the statistics on nuclear power, the idea that nuclear power is safe may strike you as either a completely ridiculous claim or an egregious understatement. If your primary familiarity with nuclear power safety is via the widely-publicized examples of Chernobyl, Three Mile Island, and more recently Fukushima, you may have the impression that nuclear power carries huge, catastrophic risks. (You may also be confusing nuclear power with nuclear weapons—nuclear weapons are indeed the greatest catastrophic risk on Earth today, but equating the two is like equating automobiles and machine guns because both of them are made of metal and contain lubricant, flammable materials, and springs.)

But in fact nuclear energy is astonishingly safe. Indeed, even those examples aren’t nearly as bad as people have been led to believe. Guess how many people died as a result of Three Mile Island, including estimated increased cancer deaths from radiation exposure?

Zero. There are zero confirmed deaths and the consensus estimate of excess deaths caused by the Three Mile Island incident by all causes combined is zero.

What about Fukushima? Didn’t 10,000 people die there? From the tsunami, yes. But the nuclear accident resulted in zero fatalities. If anything, those 10,000 people were killed by coal—by climate change. They certainly weren’t killed by nuclear.

Chernobyl, on the other hand, did actually kill a lot of people. Chernobyl caused 31 confirmed direct deaths, as well as an estimated 4,000 excess deaths by all causes. On the one hand, that’s more than 9/11; on the other hand, it’s about a month of US car accidents. Imagine if people had the same level of panic and outrage at automobiles after a month of accidents that they did at nuclear power after Chernobyl.

The vast majority of nuclear accidents cause zero fatalities; other than Chernobyl, none have ever caused more than 10. Deepwater Horizon killed 11 people, and yet for some reason Americans did not unite in opposition against ever using oil (or even offshore drilling!) ever again.

In fact, even that isn’t fair to nuclear power, because we’re not including the thousands of lives saved every year by using nuclear instead of coal and oil.

Keep in mind, the WHO estimates 10 to 100 million excess deaths due to climate change over the 21st century. That’s an average of 100,000 to 1 million deaths every year. Nuclear power currently produces about 11% of the world’s energy, so let’s do a back-of-the-envelope calculation for how many lives that’s saving. Assuming that additional climate change would be worse in direct proportion to the additional carbon emissions (which is conservative), and assuming that half that energy would be replaced by coal or oil (also conservative, using Germany’s example), we’re looking at about a 6% increase in deaths due to climate change if all those nuclear power plants were closed. That’s 6,000 to 60,000 lives that nuclear power plants save every year.

I also haven’t included deaths due to pollution—note that nuclear power plants don’t pollute air or water whatsoever, and only produce very small amounts of waste that can be quite safely stored. Air pollution in all its forms is responsible for one in eight deaths worldwide. Let me say that again: One in eight of all deaths in the world is caused by air pollution—so this is on the order of 7 million deaths per year, every year. We burn our way to a biannual Holocaust. Most of this pollution is actually caused by burning wood—fireplaces, wood stoves, and bonfires are terrible for the air—and many countries would actually see a substantial reduction in their toxic pollution if they switched to oil or even coal in favor of wood. But a large part of that pollution is caused by coal, and a nontrivial amount is caused by oil. Coal-burning factories and power plants are responsible for about 1 million deaths per year in China alone. Most of that pollution could be prevented if those power plants were nuclear instead.

Factor all that in, and nuclear power currently saves tens if not hundreds of thousands of lives per year, and expanding it to replace all fossil fuels could save millions more. Indeed, a more precise estimate of the benefits of nuclear power published a few years ago in Environmental Science and Technology is that nuclear power plants have saved some 1.8 million human lives since their invention, putting them on a par with penicillin and the polio vaccine.

So, I hope I’ve convinced you of the first proposition: Nuclear power plants are safe—and not just safe, but heroic, in fact one of the greatest life-saving technologies ever invented. So, why don’t people like them?

Unfortunately, I suspect that no amount of statistical data by itself will convince those who still feel a deep-seated revulsion to nuclear power. Even many environmentalists, people who could be nuclear energy’s greatest advocates, are often opposed to it. I read all the way through Naomi Klein’s This Changes Everything and never found even a single cogent argument against nuclear power; she simply takes it as obvious that nuclear power is “more of the same line of thinking that got us in this mess”. Perhaps because nuclear power could be enormously profitable for certain corporations (which is true; but then, it’s also true of solar and wind power)? Or because it also fits this narrative of “raping and despoiling the Earth” (sort of, I guess)? She never really does explain; I’m guessing she assumes that her audience will simply share her “gut feeling” intuition that nuclear power is dangerous and untrustworthy. One of the most important inconvenient truths for environmentalists is that nuclear power is not only safe, it is almost certainly our best hope for stopping climate change.

Perhaps all this is less baffling when we recognize that other heroic technologies are often also feared or despised for similarly bizarre reasons—vaccines, for instance.

First of all, human beings fear what we cannot understand, and while the human immune system is certainly immensely complicated, nuclear power is based on quantum mechanics, a realm of scientific knowledge so difficult and esoteric that it is frequently used as the paradigm example of something that is hard to understand. (As Feynman famously said, “I think I can safely say that nobody understands quantum mechanics.”) Nor does it help that popular treatments of quantum physics typically bear about as much resemblance to the actual content of the theory as the X-Men films do to evolutionary biology, and con artists like Deepak Chopra take advantage of this confusion to peddle their quackery.

Nuclear radiation is also particularly terrifying because it is invisible and silent; while a properly-functioning nuclear power plant emits less ionizing radiation than the Capitol Building and eating a banana poses substantially higher radiation risk than talking on a cell phone, nonetheless there is real danger posed by ionizing radiation, and that danger is particularly terrifying because it takes a form that human senses cannot detect. When you are burned by fire or cut by a knife, you know immediately; but gamma rays could be coursing through you right now and you’d feel no different. (Huge quantities of neutrinos are coursing through you, but fear not, for they’re completely harmless.) The symptoms of severe acute radiation poisoning also take a particularly horrific form: After the initial phase of nausea wears off, you can enter a “walking ghost phase”, where your eventual death is almost certain due to your compromised immune and digestive systems, but your current condition is almost normal. This makes the prospect of death by nuclear accident a particularly vivid and horrible image.

Vividness makes ideas more available to our memory; and thus, by the availability heuristic, we automatically infer that it must be more probable than it truly is. You can think of horrific nuclear accidents like Chernobyl, and all the carnage they caused; but all those millions of people choking to death in China don’t make for a compelling TV news segment (or at least, our TV news doesn’t seem to think so). Vividness doesn’t actually seem to make things more persuasive, but it does make them more memorable.

Yet even if we allow for the possibility that death by radiation poisoning is somewhat worse than death by coal pollution (if I had to choose between the two, okay, maybe I’d go with the coal), surely it’s not ten thousand times worse? Surely it’s not worth sacrificing entire cities full of people to coal in order to prevent a handful of deaths by nuclear energy?

Another reason that has been proposed is a sense that we can control risk from other sources, but a nuclear meltdown would be totally outside our control. Perhaps that is the perception, but if you think about it, it really doesn’t make a lot of sense. If there’s a nuclear meltdown, emergency services will report it, and you can evacuate the area. Yes, the radiation moves at the speed of light; but it also dissipates as the inverse square of distance, so if you just move further away you can get a lot safer quite quickly. (Think about the brightness of a lamp in your face versus across a football field. Radiation works the same way.) The damage is also cumulative, so the radiation risk from a meltdown is only going to be serious if you stay close to the reactor for a sustained period of time. Indeed, it’s much easier to avoid nuclear radiation than it is to avoid air pollution; you can’t just stand behind a concrete wall to shield against air pollution, and moving further away isn’t possible if you don’t know where it’s coming from. Control would explain why we fear cars less than airplanes (which is also statistically absurd), but it really can’t explain why nuclear power scares people more than coal and oil.

Another important factor may be an odd sort of bipartisan consensus: While the Left hates nuclear power because it makes corporations profitable or because it’s unnatural and despoils the Earth or something, the Right hates nuclear power because it requires substantial government involvement and might displace their beloved fossil fuels. (The Right’s deep, deep love of the fossil fuel industry now borders on the pathological. Even now that they are obviously economically inefficient and environmentally disastrous, right-wing parties around the world continue to defend enormous subsidies for oil and coal companies. Corruption and regulatory capture could partly explain this, but only partly. Campaign contributions can’t explain why someone would write a book praising how wonderful fossil fuels are and angrily denouncing anyone who would dare criticize them.) So while the two sides may hate each other in general and disagree on most other issues—including of course climate change itself—they can at least agree that nuclear power is bad and must be stopped.

Where do we go from here, then? I’m not entirely sure. As I said, statistical data by itself clearly won’t be enough. We need to find out what it is that makes people so uniquely terrified of nuclear energy, and we need to find a way to assuage those fears.

And we must do this now. For every day we don’t—every day we postpone the transition to a zero-carbon energy grid—is another thousand people dead.